Question 6 (10 points)
=) Listen
The ratio of outdoor outdoor swimmers to indoor swimmers at the recreation center
is 3:2. If the center has 55 swimmers altogether, how many of them are indoor
swimmers?
22
44
none
33

The expression for the total cost of Sal's purchases is 7x + 5y cents.

We know that Sal paid (x + 2y) cents for a quart of milk and (2x + y) cents each for three cartons of orange juice.To find the total cost of Sal's purchases we need to add the cost of the milk and the cost of the three cartons of orange juice and simplify the expression.The cost of the milk is given as (x + 2y) cents. The cost of three cartons of orange juice is (2x + y) cents each.

Therefore, the cost of three cartons of orange juice is (3 × (2x + y)) cents. To find the total cost of Sal's purchases, we add the cost of the milk and the cost of the three cartons of orange juice.(x + 2y) + (3 × (2x + y)) cents = x + 2y + 6x + 3y cents= 7x + 5y cents.

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The coefficient of determination is the square of the correlation coefficient, and the value is 0.0151

The given parameter is:

Correlation coefficient, r = 0.123

Rewrite as:

r = 0.123

Take the square of both sides

r² = 0.123²

Evaluate the square

r² = 0.015129

Approximate

r² = 0.0151

The coefficient of determination is represented by r²

Hence, the coefficient of determination is 0.0151

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Answer:

58.1 and 17

Step-by-step explanation:

For the first triangles the similarity ratio is 1:7 so x is 8.3 × 7 = 58.1

For the second triangles the similarity ratio is 1:5 so x is 3.4 × 5 = 17

Answer:

2

Step-by-step explanation:

Area = length * width * height

  4/5 * 3/2 * 5/3

=  60/30

= 2

Answer:

c

Step-by-step explanation:

i go to norcross high school btw . smh ;)

The value of exterior angle is 100

If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.

Given:

angle 1 = 30

angle 2 = 7x

exterior angle= 10x

Now using exterior angle property

10x= 7x+30

3x= 30

x=10

Hence, the exterior angle is 10x= 100 degree

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2 quart of blue paint and 5/4 quart of red paint is needed to make 3 1/4 quart purple paint

An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.

2/5 quart of blue paint is mixed with 1/4 quart of red paint to make purple paint. Hence:

Ratio of blue paint to red paint = (2/5) : (1/4) = 8 : 5

Therefore for 3 1/4 quart of purple paint:

Amount of blue paint = (8/13) * 3 1/4 = (8/13) * 13/4 = 2 quart

Amount of red paint = (5/13) * 3 1/4 = (5/13) * 13/4 = 5/4 quart

2 quart of blue paint and 5/4 quart of red paint is needed to make the purple paint

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Answer: To find the gradient of a curve at a given point, we need to find the derivative of the function with respect to x and then evaluate it at the desired x-coordinate.

Given the function y = 3x^4 - 2x^2 + 5x - 2, we can find its derivative dy/dx as follows:

dy/dx = d/dx(3x^4) - d/dx(2x^2) + d/dx(5x) - d/dx(2)

Taking the derivative of each term:

dy/dx = 12x^3 - 4x + 5

Now, let's evaluate the derivative at the given points:

Point (0, -2):

Substituting x = 0 into the derivative:

dy/dx = 12(0)^3 - 4(0) + 5

dy/dx = 0 - 0 + 5

dy/dx = 5

Therefore, the gradient at (0, -2) is 5.

Point (1, 4):

Substituting x = 1 into the derivative:

dy/dx = 12(1)^3 - 4(1) + 5

dy/dx = 12 - 4 + 5

dy/dx = 13

Therefore, the gradient at (1, 4) is 13.

We need to substitute the value -4 in the place of x, that is

By the law of exponents, this can be rewritten as

which gives

which corresponds to option B

With a 12% housekeeping gratuity, the hotel bill for 4 nights comes to $891.52.

"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."

We always count the unit or amount value first and then calculate the more or less amount value.

For this reason, this procedure is called a unified procedure.

Many set values ​​are found by multiplying the set value by the number of sets.

A set value is obtained by dividing many set values ​​by the number of sets.

According to our question-

Total cost = Bill before tip + Tip

Total cost = $796 + $95.52

Total cost = $891.52

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Answer:

a

\(\= x  =  82 \)

b

\(s =  9.64 \)

Step-by-step explanation:

From the question we are told that

    The data is  87  91  86  82  72  91   60  77  80  79  83  96

Generally the point estimate for the mean is mathematically represented as

    \(\= x  =  \frac{\sum  x_i }{n}\)

=>  \(\= x  =  \frac{87 +91 + 86 + \cdots  + 96}{12}\)

=>    \(\= x  =  82 \)

Generally the point estimate for the standard deviation  is mathematically represented as

      \(s =  \sqrt{\frac{ \sum ( x_i  - \= x )^2 }{ n -1 } }\)

=>     \(s =  \sqrt{\frac{ ( 87 - 82  )^2 +( 91 - 82  )^2 + \cdots + ( 96 - 82  )^2  }{ 12 -1 } }\)

=>     \(s =  9.64 \)

Part(a): The required mean is 82

Part(b): The required standard deviation is 9.639

Mean:

The mean is one of the measures of central tendency.

Part(a):

The formula for finding the mean is,

\(\bar{x}=\frac{\sum x_i}{n}\)

Now, calculating the mean for the \(n=12\) observation

\(\bar{x}=\frac{87+91+86+82+72+91+60+77+80+79+83+96}{12}\\ \bar{x}=82\)

Part(b):

The formula for the standard deviation is,

\(S=\sqrt{\frac{\sum (x_i-\bar{x})^2}{n-1} }\)

Substituting the given values into the above formula we get,

\(S=\sqrt{\frac{((87-82)^2+(91-82)^2)+(86-82)^2+(82-82)^2+(72-82)^2+(91-82)^2+(60-82)^2+(77-82)^2+...+(96-82)^2}{12-1} } \\S=9.639\)

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Answer:45%

Step-by-step explanation:

The expression shows the total amount in Diego's savings account after m months is 500 - 20m.

What is the total amount?

Two numbers are added together to form the sum. It is simple to figure out the sum of small integers. You can add two numbers using your fingertips. When two or more numbers are added together, a mathematical sum or maths sum is the outcome. It is the sum of the numbers when they are added up.

Here, we have

Given: Deigo has $500 in his saving account each month he takes out $20 to pay for karate class.

Let m be the number of months. Write an expression to show the total amount in Diego's savings account after m months.

The expression:

= 500 - 20m

Here m is the number of months

Hence, the expression shows the total amount in Diego's savings account after m months is 500 - 20m.

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The trigonometric equations has the following solutions: x = 0 + j · π or x = 0.352π + j · π or x = - 0.352π + j · π, where j is a non-negative whole number.

In this problem we find the case of a trigonometric equation, whose solutions on the interval [0, 2π] must be found. This can be done by both algebra properties and trigonometric formulae. First, write the entire expression:

tan² x · sec² x + 2 · sec² x - tan² x = 2

Second, use trigonometric formulas to reduce the number of trigonometric functions:

tan² x · (tan² x + 1) + 2 · (tan² x + 1) - tan² x = 2

Third, expand the equation:

tan⁴ x + tan² x + 2 · tan² x + 2 - tan² x = 2

tan⁴ x + 2 · tan² x = 0

Fourth, factor the expression:

tan² x · (tan² x - 2) = 0

tan² x = 0 or tan² x = 2

tan x = 0 or tan x = ± √2

Fifth, determine the solutions to trigonometric equation:

x = 0 + j · π or x = 0.352π + j · π or x = - 0.352π + j · π, where j is a non-negative whole number.

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(Part 1)  The expression \(18\sqrt{8}\) can be written in the form \(a\sqrt{b}\) as \(36\sqrt{2}\), where a and b are integers and b is as small as possible.

(Part 2)  The expression \(8\sqrt{18}\) can be written in the form \(a\sqrt{b}\) as \(16\sqrt{3}\).

(Part 3)  The expression \(18\sqrt{8}\) - \(8\sqrt{18}\) + \(\sqrt{n}\) is equal to (\(36\sqrt{2}\) - \(16\sqrt{3}\)) + \(\sqrt{n}\).

(Part 1) Expressing \(18\sqrt{8}\) in the form \(a\sqrt{b}\), where a and b are integers and b is as small as possible:

We can factor \(\sqrt{8}\) as \(\sqrt{2}\)* \(\sqrt{4}\)

So, \(18\sqrt{8}\)= 18 * \(\sqrt{2}\) *\(\sqrt{4}\) = 18 *\(\sqrt{2}\) * 2 = \(36\sqrt{2}\)

So the expression \(18\sqrt{8}\) can be written in the form \(a\sqrt{b}\) as \(36\sqrt{2}\), where a = 36 and b = 2.

(Part 2) Expressing \(8\sqrt{18}\) in the form \(a\sqrt{b}\), where a and b are integers and b is as small as possible:

We can factor \(\sqrt{18}\) as \(\sqrt{3}\) * \(\sqrt{6}\)

So, \(8\sqrt{18}\) = 8 * \(\sqrt{3}\) * \(\sqrt{6}\)

\(8\sqrt{18}\)= 8 * \(\sqrt{3}\) * \(\sqrt{2}\) * \(\sqrt{3}\)

\(8\sqrt{18}\)= 8 *\(\sqrt{6}\)* \(\sqrt{2}\)

\(8\sqrt{18}\)= 8 * \(\sqrt{2}\) * \(\sqrt{6}\)

\(8\sqrt{18}\)= 8 * 2 * \(\sqrt{3}\)

\(8\sqrt{18}\)= \(16\sqrt{3}\)

So the expression \(8\sqrt{18}\) can be written in the form \(a\sqrt{b}\) as \(16\sqrt{3}\), where a = 16 and b = 3.

(Part 3) \(18\sqrt{8}\) - \(8\sqrt{18}\) + \(\sqrt{n}\):

We can substitute the simplified forms of \(18\sqrt{8}\) and \(8\sqrt{18}\) from parts 1 and 2 into this expression:

\(18\sqrt{8}\) - \(8\sqrt{18}\) + \(\sqrt{n}\) = \(36\sqrt{2}\) - \(16\sqrt{3}\) + \(\sqrt{n}\) = (\(36\sqrt{2}\) - \(16\sqrt{3}\)) + \(\sqrt{n}\).

So, the expression \(18\sqrt{8}\) - \(8\sqrt{18}\) + \(\sqrt{n}\) is equal to (\(36\sqrt{2}\) - \(16\sqrt{3}\)) + \(\sqrt{n}\) where n is an unknown constant.

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Answer:

C.

Step-by-step explanation:

If you graph it, you can see that the lines are parallel.

Answer:

22,873.35

Step-by-step explanation:

A=p+I where P(principal) = 18,000

I(interest) = 4,873.35

Answer:

A = 22,775

Step-by-step explanation:

A = amount after 6 years

P = 18,000

r = 4%  (in decimal = 0.04)

t = 6 years

A = 18,000 ( 1 + 0.04)^6

A = 22,775

Answer:

f(x) = 2x + 7

f(8) = 2(8) + 7 = 16 + 7 = 23

The first option is correct. When the polynomial -3x² + 2x - 4 - (-2x² - x + 4) is simplified the result is -x² + 3x - 8.

A polynomial is a mathematical expression consisting of variables and coefficients, which are combined using arithmetic operations such as addition, subtraction, and multiplication.

We shall simply the polynomial -3x² + 2x - 4 - (-2x² - x + 4) as follows:

open bracket;

-3x² + 2x - 4 + 2x² + x - 4

group like terms;

-3x² + 2x² + 2x + x - 4 - 4

- x² + 3x - 8.

Therefore, the polynomial -3x² + 2x - 4 - (-2x² - x + 4) is simplified to give the result is -x² + 3x - 8.

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Answer:

2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

It’s 2 because

2 has 6 sides and the net has 6 squares

picture folding up the net. You’ll h]get number 2

Answer:

4x + 2y = 8

: P( 0; 4) & Q( 2; 0)

The difference of the algebraic expressions is 3x² - 11x + 4

An algebraic expression is an expression that is made up of variables and constants, along with algebraic operations like addition, subtraction, square root, etc.

The difference of two algebraic expressions means the subtraction of the expressions. That is:

(-4x+3) - (7x - 3x² - 1) = -4x+3 -7x+3x²+1

                                 =  3x² - 11x + 4

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Answer:

7:16

Step-by-step explanation:

The answer will be laid out like this-

girls : total children

This question is asking for the ratio of girls to the total number of kids, and we already know that there are 7 girls, so that already fills in the first part of the answer! Now we have to add both the girls and the boys up for the rest of the answer.

7 + 9 = 16

Now we just fill in the blanks for the layout we just created and we have our answer- 7:16!

Hope this helps! Have a lovely day! :)

Answer:

\(f(a) = 2a + 8\)

\(f(x + h) = 2x + 2h + 8\)

\(\frac{f(x + h) - f(x)}{h} = 2\)

Step-by-step explanation:

Given

\(f(x) = 2x + 8\)

Required

\(f(a)\)

\(f(x + h)\)

\(\frac{f(x + h) - f(x)}{h}\)

Solving for f(a)

Substitute a for x in the given parameter

\(f(x) = 2x + 8\) becomes

\(f(a) = 2a + 8\)

Solving for f(x+h)

Substitute x + h for x in the given parameter

\(f(x + h) = 2(x + h) + 8\)

Open Bracket

\(f(x + h) = 2x + 2h + 8\)

Solving for \(\frac{f(x + h) - f(x)}{h}\)

Substitute 2x + 2h + 8 for f(x + h), 2x + 8 fof f(x)

\(\frac{f(x + h) - f(x)}{h}\) becomes

\(\frac{2x + 2h + 8 - (2x + 8)}{h}\)

Open Bracket

\(\frac{2x + 2h + 8 - 2x - 8}{h}\)

Collect Like Terms

\(\frac{2x - 2x+ 2h + 8 - 8}{h}\)

Evaluate the numerator

\(\frac{2h}{h}\)

\(2\)

Hence;

\(\frac{f(x + h) - f(x)}{h} = 2\)

Therefore, it is not even chance, but it is also not very unlikely. It is moderately likely that a yellow marble will be selected on the first draw.

Probability is a branch of mathematics that deals with the study of random events and their likelihood of occurring. It is a measure of the likelihood or chance of an event happening. Probability is expressed as a number between 0 and 1, where 0 means the event is impossible, and 1 means the event is certain.

In other words, probability is a way of quantifying uncertainty. It is used in various fields, such as statistics, physics, finance, engineering, and more, to help make predictions and decisions based on uncertain information. Probability theory provides a set of rules and tools for analyzing and manipulating random variables and events, and for calculating the probability of complex events.

The likelihood of a yellow marble being selected on the first draw can be calculated by dividing the number of yellow marbles by the total number of marbles in the bag:

likelihood of selecting a yellow marble = number of yellow marbles / total number of marbles

So, in this case, the likelihood of selecting a yellow marble on the first draw is:

likelihood of selecting a yellow marble = 2 / (3 + 2 + 1) = 2/6 = 1/3

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Answer:

The sum will be close to 1/4

Step-by-step explanation:

1/8+1/6 is 7/24, and 1/4th of that is 6/24, so it is very close.

Answer: The sum will be close to 1/4

Step-by-step explanation:

You can start by making the fractions have the same denominator, (8*6) which gets you 48

You then want to use the butterfly method, so 1/8 becomes 6/48 and 1/6 becomes 8/48. You then add these up to 14/48.

12/48 is 1/4, and 14/48 is close to 12/48, thus making the answer the first option.

Step-by-step explanation:

The given equation is :

2x+7y=11

We need to tell the point (-5,3) lies on the graph of the above equation of not.

Put x = -5 and y = 3 in the LHS of the above equation.

LHS = 2x+7y

= 2(-5)+7(3)

= -10 +21

= 11

It means, when we put  x = -5 and y = 3 in the above equation, we get 11. Hence, (-5,3) lies on the graph of the equation.